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A study on monotone self-dual Boolean functions

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Abstract

This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form (IDNF) do not have more variables than disjuncts. Monotone self-dual Boolean functions in IDNF with the same number of variables and disjuncts are examined. An algorithm is proposed to test whether a monotone Boolean function in IDNF with n variables and n disjuncts is self-dual. The runtime of the algorithm is O(n3).

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References

  1. Altun, M., Riedel, M.D. Lattice-based computation of Boolean functions. In: Design Automation Conference, 2010, 609–612

    Google Scholar 

  2. Altun, M., Riedel, M.D. Logic synthesis for switching lattices. IEEE Transactions on Computers, 61(11): 1588–1600 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boros, E., Elbassioni, K., Gurvich, V., Khachiyan, L. Generating maximal independent sets for hypergraphs with bounded edge-intersections. LATIN 2004: Theoretical Informatics, 488–498, 2004

    Chapter  Google Scholar 

  4. Boros, E., Hammer, P., Ibaraki, T., Kawakami, K. Polynomial-time recognition of 2-monotonic positive boolean functions given by an oracle. SIAM Journal on Computing, 26(1): 93–109 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Eiter, T., Gottlob, G. Identifying the minimal transversals of a hypergraph and related problems. SIAM Journal on Computing, 24(6): 1278–1304 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Eiter, T., Gottlob, G. Hypergraph transversal computation and related problems in logic and AI. Lecture Notes in Computer Science 2424: 549–564 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Eiter, T., Makino, K., Gottlob, G. Computational aspects of monotone dualization: A brief survey. Discrete Applied Mathematics, 156(11): 1952–2005 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Elbassioni, K. On the complexity of monotone dualization and generating minimal hypergraph transver-sals. Discrete Applied Mathematics, 156(11): 2109–2123 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Elbassioni, K., Rauf, I. Polynomial-time dualization of r-exact hypergraphs with applications in geometry. Discrete Mathematics 310(17): 2356–2363 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fredman, M.L., Khachiyan, L. On the complexity of dualization of monotone disjunctive normal forms. Journal of Algorithms, 21(3): 618–628 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gaur, D.R., Krishnamurti, R. Self-duality of bounded monotone boolean functions and related problems. In: Algorithmic Learning Theory. Springer-Verlag, 2000, 209–223

    Chapter  Google Scholar 

  12. Gaur, D.R., Krishnamurti, R. Self-duality of bounded monotone Boolean functions and related problems. Discrete Applied Mathematics, 156(10): 1598–1605 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gottlob, G. Deciding monotone duality and identifying frequent itemsets in quadratic logspace. arXiv: 1212.1881 (2012)

    Google Scholar 

  14. Karasan, O.E. Incremental polynomial time dualization of quadratic functions and a subclass of degree-k functions. Annals of Operations Research, 188(1): 251–261 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Makino, K. Efficient dualization of O (log n)-term monotone disjunctive normal forms. Discrete Applied Mathematics, 126: 305–312 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Papadimitriou, C.H. Computational complexity. John Wiley and Sons Ltd., 2003

    MATH  Google Scholar 

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Authors and Affiliations

  1. Electronics and Communication Engineering, Istanbul Technical University, Istanbul, Turkey, 34469

    Mustafa Altun

  2. Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Marc D. Riedel

Authors
  1. Mustafa Altun
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  2. Marc D. Riedel
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Correspondence to Mustafa Altun.

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Altun, M., Riedel, M.D. A study on monotone self-dual Boolean functions. Acta Math. Appl. Sin. Engl. Ser. 33, 43–52 (2017). https://doi.org/10.1007/s10255-017-0633-x

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  • DOI: https://doi.org/10.1007/s10255-017-0633-x

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